"Both teams didn't create much," Leicester captain Wes Morgan told Sky Sports. "It was tough with the quick turnaround, playing on Saturday, then again today.
"On reflection, 0-0 is a good result for us and a clean sheet is always good."
Middlesbrough, now 16th on 19 points, enjoyed the better of the action and threatened through Adama Traore, the game's outstanding individual, but he struggled to find an end product to accompany his scintillating work out wide.
"It's a good result for us," Boro coach Aitor Karanka told reporters. "I'm really pleased with the performance.
"We showed that we are better than them and we can't forget they are a Champions League side and the Premier League champions. We have to continue to be organised and not concede goals."
Gaston Ramirez fired an 83rd-minute effort into the side netting, but Boro were unadventurous and have now won just once in their last six matches.
Leicester kept consecutive clean sheets for the first time since April but the champions, who moved seven points clear of the drop zone ahead of the matches later on Monday, are still awaiting their first away win of the season.
(Reporting by Ed Dove, editing by Ed Osmond)
